Omnipresent polynomials
Algebra, analysis: the double nature of polynomials makes them essential. In algebra, they act a bit like numbers; we can add them, multiply them, divide them, factor them... In analysis, they metamorphose into functions. Their simplicity and flexibility allow them to facilitate the notion of integration and to approximate other, more complex functions, with a fascinating property: their ability to "hug" the graph of any differentiable function on an interval. And polynomials haven't had their last word! They still hold many surprises for anyone who ventures into their study.
All articles in this folder
Between algebra and analysis: an indispensable world
Polynomials belong to both algebra and analysis, which can lead to all kinds of confusion! This dual nature offers a simple way to explain the subtle differences between variables, unknowns and indeterminates.
Approximating a function and following its curve
Assuming that a function is a polynomial yields useful approximation formulas. A complicated function can thus be replaced by a polynomial, simplifying most calculations. More surprisingly, interpolation lies at the heart of a secret-sharing technique.
In search of asymptotes
Euclidean division of polynomials is very useful in analysis! The proof, with three examples